University of California, Los Angeles 4 credits Mathematics
Lecture, three hours; discussion, one hour. Homotopy theory: fundamental group, covering spaces, Van Kampen’s theorem. Homology theory: singular homology, simplicial homology, homotopy invariance, relative homology, excision and Mayer-Vietoris, functoriality, relationship to the fundamental group, calculations with cellular complexes (CW complexes). Cohomology theory: singular cohomology, universal coefficient theorem, cup products. S/U or letter grading.
Our subject experts help with essays, research papers, case studies, discussion posts, and capstone projects for these programs — written from scratch to your course requirements.
Program and course information is reproduced from each university's published academic catalog for informational purposes and may change. Always confirm current requirements with your university. We are an independent academic support service and are not affiliated with or endorsed by the universities listed.
Expert guides on essay writing, citation styles, study skills, and academic success.
View All Articles
Learn how to write a good research question for a paper. Narrow your topic, identify a research problem, and create a focused question with practical examples.
Learn how to choose a research topic you can actually research. Discover how to narrow broad ideas, find reliable sources, and develop a focused research question.
Learn how to cite sources in a research paper using APA, MLA, and Chicago styles, with in-text citation examples and reference-list tips.